Galois extensions for trivial group

This article gives specific information, namely, Galois extensions, about a particular group, namely: trivial group.
View Galois extensions for particular groups | View other specific information about trivial group

Given a Galois extension of fields $L/K$, the Galois group for the extension is the trivial group if and only if $L=K$.

For a Galois extension of fields $L/K$, the smallest subfield of $L$ containing $K$ possible, namely $K$, corresponds to the smallest subgroup of the Galois group possible, the trivial group.